Corrected entry: Anna's mother died in the boathouse caused by the fire. She and her belongings were burnt. But when Anna comes home, she finds her mother's bell, which was attached to her wrist at the time of the fire. It was tied onto a string, which would have been burnt to ash, but the string is still intact along with the bell being in prime condition.
Corrected entry: When Anna goes down to the boathouse at night, because she hears her mother's bell, the outdoor light is on. Then when she sees her mother the light is off, but when Alex comes in the light turns back on. In the next shot it's off again.
Correction: Since no "real" person acknowledges the bell, we can presume it is part of Anna's delusion.
JAGwire